When the smaller of two consecutive integers is added to three times the larger, the result is 31. find the integers.

Let x be the smaller number and y the larger:

As the numbers are consecutive y - x = 1
And 3y + x = 31  (3 times the large added to the smaller)

From the first equation y = x + 1
By substituting:
3(x + 1) + x = 31
3x + 3 + x = 31
4x = 28
x = 7

y = x + 1
y = 7 + 1 = 8